is there an easier way to use a still from a movie as a texture?
It's very easy to choose just one frame form a video to be used:

look for the frame controls in the texture panel.



Here's an example of how to use it:

Frames (how many frames you want to use from the video file, in this case just 1 since we want to freeze it, even if the original video has thousands of frames)

Start (at what point in the blender time line should this image start? In this case it will start from the very first frame of the blender project.)

Offset Set the frame number of the particular frame you want to freeze, in this case the frame with the smile is 1110.

In other words, blender will just use one image as a texture and will play only frame 1110 of the video file on every frame of the blender project starting from the beginning.

For Cycles the same options are available on the Image Texture node.